the introduction of derivatives on the dow jones industrial average and their impact on the...

THE INTRODUCTION OF

DERIVATIVES ON THE DOW

JONES INDUSTRIAL AVERAGE

AND THEIR IMPACT ON

THE VOLATILITY OF

COMPONENT STOCKS

SHAFIQUR RAHMAN

This article examines the impact of trading in the Dow Jones IndustrialAverage (DJIA) index futures and futures options on the conditionalvolatility of component stocks. It investigates the contention that theintroduction of futures and futures options on the DJIA could increasevolatility in the 30 stocks comprising the DJIA. The conditional volatilityof intraday returns for each stock before and after the introductionof derivatives is estimated with the Generalized AutoregressiveConditional Heteroscedasticity (GARCH) model. Estimated param-eters of conditional volatility in prefutures and postfutures periods arethen compared to determine if the estimated parameters have changedsignificantly after the introduction of the various derivatives. The results

The author is grateful to Robert I. Webb, the editor, and an anonymous reviewer for helpful com-ments and valuable suggestions. The author thanks Phil Gerrard and Julia Sawicki for helpful dis-cussions and comments. Nanyang Business School at Nanyang Tech University provided partialfunding for this research. The usual disclaimer applies.For correspondence, Shafiqur Rahman, Division of Banking and Finance, Nanyang BusinessSchool, Nanyang Tech University, Singapore 639798; e-mail: [email protected]

Received January 2000; Accepted October 2000

� Shafiqur Rahman is a Professor of Banking and Finance in the School of BusinessAdministration at Portland State University in Portland, Oregon, and a VisitingProfessor of Banking and Finance in the Nanyang Business School at Nanyang TechUniversity in Singapore.

The Journal of Futures Markets, Vol. 21, No. 7, 633–653 (2001)© 2001 by John Wiley & Sons, Inc.

suggest that the introduction of index futures and futures options on theDJIA has produced no structural changes in the conditional volatilityof component stocks. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark21: 633–653, 2001

INTRODUCTION

The issue of the impact of derivatives trading on stock market volatilityhas received considerable attention in recent years, particularly after thestock market crash of 1987 and the minicrash of 1989 (e.g., Campbell,1991; Kawaller, Koch, & Koch 1990; Report of the Presidential TaskForce on Market Mechanisms, 1988).1 Although many factors con-tribute to stock market volatility, there is concern about the impact ofderivative securities, particularly index futures and options, on theunderlying spot market. One perception is that derivatives trading isresponsible for higher stock market volatility (e.g., Conrad, 1989; Harris,Sofianos, & Shapiro, 1994). It is argued that derivatives encourage spec-ulation, which destabilizes the spot market. The alleged destabilizationtakes the form of higher spot market volatility. This has led to the sug-gestion that there is a need for closer regulation and supervision of thederivatives industry.2

On October 6, 1997, the Chicago Board of Trade (CBOT) openedits newest pit for trading in futures and futures options on the Dow JonesIndustrial Average (DJIA). This article examines the impact of trading inthe DJIA index futures and futures options on the volatility of compo-nent stocks. Specifically, it investigates whether the introduction offutures and futures options on the DJIA increases volatility of the30 stocks comprising the DJIA. The introduction of derivative productsmay increase volatility in component stocks. This is because the spot andfutures markets are linked through risk transfer (hedging) and pricediscovery, two major contributions of the futures markets to economic

634 Rahman

1The Report of the Presidential Task Force on Market Mechanisms (1988), popularly known as theBrady Commission Report, attributed the sharp fall in stock prices during the 1987 crash to pro-gram trading or, more specifically, the derivative-based trading strategies known as index arbitrageand portfolio insurance. It may be pointed out that derivatives trading was not blamed for the marketcrash during the 1997 Asian financial crisis. Unlike during the 1987 and 1989 crashes, market par-ticipants did not point the finger at derivatives trading as the potential source of market instability.See Cheng, Fung, and Chan (2000) for an analysis of the Asian financial crisis.2The regulatory proposals for reform advanced by the Brady Commission Report include a singleagency to coordinate regulatory issues across all financial markets, a unified clearing system for allfinancial markets, consistent margin requirements in the cash and futures markets, circuit breakermechanisms such as price limits and planned trading halts, and integrated information systemsacross related financial markets. There is continuing action on all of these fronts, and much hasalready been implemented.

activity.3 The index arbitrageurs could use these markets to take advan-tage of price discrepancies between the DJIA spot price and the DJIAfutures price.

This study employs the Generalized Autoregressive ConditionalHeteroscedasticity (GARCH) model to estimate the conditional volatility ofintraday returns before and after the introduction of derivatives.Estimated parameters of conditional volatility in prefutures and postfu-tures periods are then compared to determine if the estimated parame-ters have changed significantly after the introduction of derivatives. Theresults suggest that the introduction of index futures and futures optionson the DJIA has produced no structural changes in the conditionalvolatility of component stocks.

Investigations of the type conducted in this article are of interestbecause they can provide useful information on the efficiency of thefutures markets and can be useful to regulators in designing regulations.The extent to which the futures markets are to be regulated depends onthe precise impact of futures trading on spot market volatility. Increasedspot market volatility resulting from futures trading may suggest a needfor more regulations.

Conversely, increased spot market volatility due to a liquid and effi-cient market resulting from futures trading could imply that more regu-lations might reduce the benefits of futures trading.

REVIEW OF THE LITERATURE

Despite the public outcry concerning increasingly volatile stock prices dueto the introduction of derivatives, the empirical evidence regarding thisissue is far from conclusive. Some studies find no evidence of increasedvolatility associated with the introduction of derivatives trading (Becketti& Roberts, 1990; Chatrath, Ramchander, & Song, 1995; Darrat &Rahman, 1995; Edwards, 1988a, 1988b; Fortune, 1989; Galloway &Miller, 1997; Kamara, Miller, & Siegel, 1992; Schwert, 1990). Otherstudies report the opposite conclusion (Chang, Cheng, & Pinegar, 1999;Gilbert, 1989; Harris, 1989; Maberly, Allen, & Brorsen, 1991).

Introduction of Derivatives on the DJIA 635

3Witherspoon (1993) described how the price discovery function of futures markets impacts the spotmarket volatility. The author pointed out that the extent to which price discovery by futures marketsimpacts the spot market depends on the levels of dominance by price discovery over the spot market:

If price discovery by futures exceeds certain critical threshold levels of dominance, then cash marketautocorrelation and long-term volatility are increased. On the other hand, if price discovery by futuresis not excessive, it leads to lower long-term volatility, more liquidity, and better efficiency. (p. 470)

Pizzi, Economopoulos, and O’Neill (1998) examined price discovery in the S&P 500 spot andfutures indexes with intraday data.

From a theoretical viewpoint, the volatility in the spot market caneither increase or decrease over time on the basis of the underlyingassumptions that are made. Most empirical studies have examined theimpact of index futures and index options by comparing the uncondition-al variance of returns before and after the introduction of futures andoptions. The introduction of stock index futures trading may lead to achange in the speed of information flow to the stock market. To examinethe effects of futures trading on spot market volatility, several studies(Antoniou & Homes, 1995; Antoniou, Holmes, & Priestley, 1998; Baldauf& Santoni, 1991; Lee & Ohk, 1992; Pericli & Koutmos, 1997) used amodel that recognized the temporal dependence of stock return volatility.

Baldauf and Santoni (1991) tested for the presence ofAutoregressive Conditional Heteroscedasticity (ARCH) effects in dailystock returns, controlled for these effects by modeling them, and testedto check whether model parameters shifted after the institution of pro-gram trading. They found no evidence of a shift in the model parameters.Lee and Ohk (1992) examined the effects of introducing index futurestrading on stock return volatility in Australia, Hong Kong, Japan, theUnited Kingdom, and the United States of America. They found thatstock volatility increased significantly shortly after the listing of the stockindex futures, with the exception of the stock markets in Australia andHong Kong. Using U.K. data, Antoniou and Holmes (1995) modeledvolatility as a GARCH process and found a significant increase in cashmarket volatility after the introduction of the Financial Times StockExchange (FTSE) 100 index in 1984. Pericli and Koutmos (1997), usingan exponential GARCH model, found that the volatility of the Standard &Poor’s (S&P) 500 index decreased after the introduction of futures trad-ing. Antoniou et al. (1998) examined the impact of futures trading onthe volatility of S&P 500 index with the asymmetric GARCH model pro-posed in Glosten, Jagannathan, and Runkle (1993). Their results suggestthat the introduction of futures has not had a detrimental effect on theunderlying spot market.

This article contributes to the ongoing debate regarding the impactof index futures and options on the volatility of the stock market. Itextends the studies of Baldauf and Santoni (1991), Lee and Ohk (1992),Antoniou and Holmes (1995), Pericli and Koutmos (1997), and Antoniouet al. (1998). This study models the well-known tendency of stockreturns to exhibit volatility clustering (i.e., conditional heteroskedas-ticity) by using the GARCH model of Bollerslev (1986) and tests forchanges in conditional volatility after the introduction of derivatives.French, Schwert, and Stambaugh (1987) and Akgiray (1989) applied

636 Rahman

GARCH models to stock indexes. Schwert and Seguin (1990) applied theGARCH model to portfolios. Lamoureux and Lastrapes (1990) and Kimand Kon (1994) applied the GARCH model to individual stocks.

Foster (1995) employed the GARCH model for investigating thevolume–volatility relationship in the oil futures markets. Kyriacou andSarno (1999) employed the GARCH model to construct a spot marketvolatility proxy in empirically examining the dynamic relationshipbetween derivatives trading and spot market volatility with daily data forthe FTSE index in the United Kingdom. Hogan, Kroner, and Sultan(1997) used the bivariate error correction GARCH model to examine therelationship between program trading and volatility in the S&P 500 cashand futures markets. Tse (1999) used the GARCH model to examineminute-by-minute price discovery and volatility spillovers between theDJIA cash and futures markets. Baillie and Bollerslev (1990) examinedintraday volatility in foreign exchange markets with a seasonal GARCHmodel. Locke and Sayers (1993) employed the GARCH model to exam-ine the intraday variance structure of index futures return series.Andersen and Bollerslev (1997) examined the characteristics of intradayreturn volatility in the foreign exchange market and index futuresmarkets with a GARCH specification.

This article is different in several important ways from the majorityof studies that employ the standard model or the GARCH model toexamine volatility shift. First, these studies use daily observations to esti-mate volatility, whereas intraday data are used here. Given that financialmarkets display high speeds of adjustment, studies based on longer inter-vals such as daily observations may fail to capture information containedin intraday market movements. Moreover, because of modern communi-cations systems and improved technology, volatility measures based ondaily observations ignore critical information concerning intraday pricepatterns. Andersen (1996) pointed out that the focus of the marketmicrostructure literature is on intraday patterns rather than interdaydynamics.

Second, many of the studies use a single sample containing a timeseries of observations around the introduction of derivatives. These stud-ies introduce a dummy variable in the model specification to capture theimpact of the introduction of derivatives. This methodology fails to allowderivatives to mature. Newly introduced derivatives may take time tomature and have an impact on the spot market. Aggarwal (1988) arguedthat index arbitrage and other trading strategies based on derivatives donot become an important activity immediately after their introduction.In this article, two separate and independent samples are selected, and


observations around the introduction of derivatives on the DJIA areexcluded. The prefutures sample is several months before the introduc-tion of derivatives, and the postfutures sample is several months after theintroduction of derivatives. Conditional volatility for each period is com-puted and then compared to determine whether the estimated parame-ters of the model shift subsequent to the introduction of derivatives.

DATA AND METHODOLOGY

Data

The data for this study consist of transaction prices for the 30 stockscomprising the DJIA. Intraday transaction data (quotes) come fromthe New York Stock Exchange (NYSE) trade and quote database.Transaction prices for April through June 1997 (prefutures period) andApril through June 1998 (postfutures period) are used. A 3-month sam-ple for prefutures and postfutures periods are matched to avoid any sea-sonality or month-of-the-year effects associated with calendar months.Each trading day is partitioned into 5-min intervals, beginning with theopening of the NYSE at 9:30 a.m. Eastern Standard Time. From thedata, 5-min interval returns are computed. Because returns are comput-ed within each day with only intraday prices, overnight returns are notincluded in any of these series.

Following Stoll and Whaley (1990a), I also excluded from the analy-sis the first two 5-min returns. Stoll and Whaley (1990b) reported thatthe average time to open for stocks in the S&P 500 index (average timeelapsed between the exchange opening and the opening transaction) isbetween 5 and 7 min. Prices during these intervals may reflect the staleclosing price of the previous day. Disregarding the first two 5-min returnobservations each day, therefore, mitigates the effects of stale priceinformation.

Methodology

The natural log of the price relative is computed for 5-min intervals togenerate a time series of 5-min returns [rt � ln(Pt�Pt�1)], where Pt andPt�1 represent price at time t and t � 1, respectively. The GARCH (1,1)specification is employed because it has been shown to be a parsimo-nious representation of conditional variance that adequately fits manyhigh-frequency time series (see Bollerslev, 1987, and Engle, 1993, fordetails). Akgiray (1989) estimated volatility with various ARCH and

638 Rahman

GARCH specifications and found that the GARCH (1,1) model per-formed best. The test results reported in the next section confirm this.The GARCH (1,1) model for conditional volatility of the 5-min returnseries can be specified as follows:

(1)

where ht is the conditional variance (volatility) of rt at time t; ao is a con-stant; a1 is a coefficient that relates the lagged value of the squaredreturn, to current volatility; and a2 is a coefficient that relates cur-rent volatility to the volatility of the previous period. After the volatilityequation (Equation 1) is estimated for both sample periods (i.e., prefu-tures and postfutures), conditional volatilities for the two periods arecompared to determine if they differ significantly.

EMPIRICAL RESULTS

As a step toward determining whether the introduction of derivatives haschanged the spot market volatility, actual variances and mean values ofthe 5-min returns for the 30 stocks during prefutures and postfuturessample periods are compared. Table I presents sample means and vari-ances of the 5-min returns for the 30 stocks for both periods. Visualinspections of the set of return variances for the two periods do notindicate significant changes in volatility between the prefutures andpostfutures periods for the overall sample. For a closer examination ofprefutures and postfutures conditional volatility, the GARCH model isfitted to the data.

To justify fitting the GARCH model to the data, the distributionalproperties of the intraday return series for both sample periods are exam-ined first. The results for the April through June 1998 period are report-ed here. The various descriptive statistics are reported in Tables IIand III in addition to the sample means and variances reported inTable I. These wide ranges of statistics provide a conclusive rejection ofthe hypothesis that the 5-min return series of the DJIA stocks are strictwhite-noise processes. The sample mean of each series is indistinguish-able from 0 at the .01% significance level.4 All series exhibit statisticallysignificant skewness and excess kurtosis (�3) at the .01% level. The chi-square goodness-of-fit test for normality is computed by the entire 5-minreturn series for each stock being divided into 60 groups. The null

r2t�1,

ht � ao � a1r˛

2t�1 � a2 ht�1


4Sample sizes vary from 4924 to 5156. Lindley (1957) suggested using lower significance levels forlarge sample sizes. All tests in this article use the significance level .01% to avoid Lindley’s paradox.

hypothesis of normality is rejected at the .01% significance level for all30 stocks with the test statistic of chi square with 57 degrees of freedom.

To test the hypothesis of independence, a test of white-noiseprocess given by the Ljung–Box–Pierce (Box & Pierce, 1970; Ljung &Box, 1978) portmanteau test statistics is used. The test statistics for lags6, 12, and 24, [denoted LB(6), LB(12), and LB(24), respectively] arereported in Table III. LB(m) is asymptotically distributed as chi squarewith m degrees of freedom. The critical values for LB(6), LB(12), andLB(24) at the .01% significance level are 27.86, 39.13, and 58.61,respectively. The null hypothesis of strict white noise is rejected in mostcases. This implies that the 5-min return series are not made up of inde-pendent variates.

640 Rahman

TABLE I

Sample Means and Variances for Pre- and Postfutures Periods

Identification1997 1998

(I.D.) No. Security M Variance M Variance

1 AT&T �2.67 � 10�7 1.13 � 10�5 �2.84 � 10�5 7.58 � 10�6

2 Allied Signal 3.35 � 10�5 4.6 � 10�6 1.30 � 10�5 8.73 � 10�6

3 Alcoa 2.20 � 10�5 3.85 � 10�6 �9.12 � 10�6 3.39 � 10�6

4 American Express 4.42 � 10�5 6.51 � 10�6 4.18 � 10�5 5.47 � 10�6

5 Boeing 1.20 � 10�5 5.91 � 10�6 �3.01 � 10�5 6.59 � 10�6

6 Caterpillar 5.86 � 10�5 3.77 � 10�6 �8.15 � 10�6 5.21 � 10�6

7 Chevron 1.29 � 10�5 4.83 � 10�6 5.79 � 10�6 3.02 � 10�6

8 Coca-Cola 3.50 � 10�5 9.47 � 10�6 1.24 � 10�5 6.7 � 10�6

9 Du Pont 2.02 � 10�5 5.95 � 10�6 �1.91 � 10�6 5.58 � 10�6

10 Kodak 1.93 � 10�6 4.21 � 10�6 2.26 � 10�5 3.96 � 10�6

11 Exxon 2.72 � 10�5 7.78 � 10�6 9.28 � 10�6 3.59 � 10�6

12 GE 5.30 � 10�5 6.56 � 10�6 1.15 � 10�5 4.27 � 10�6

13 GM 2.21 � 10�6 5.44 � 10�6 0.00 3.92 � 10�6

14 Goodyear Tire 3.77 � 10�5 4.19 � 10�6 �3.19 � 10�5 3.21 � 10�6

15 H-P 7.16 � 10�6 1.46 � 10�5 1.69 � 10�5 8.14 � 10�6

16 IBM 0.00 8.10 � 10�6 1.98 � 10�5 4.11 � 10�6

17 Int’l Paper 4.40 � 10�5 7.29 � 10�6 �1.82 � 10�5 6.17 � 10�6

18 J.P. Morgan 1.40 � 10�5 3.40 � 10�6 �2.77 � 10�5 4.05 � 10�6

19 Johnson & Johnson 3.84 � 10�5 5.36 � 10�6 1.86 � 10�6 4.08 � 10�6

20 McDonald’s 5.65 � 10�6 4.61 � 10�6 2.76 � 10�5 3.39 � 10�6

21 Merck 3.27 � 10�5 4.86 � 10�6 8.92 � 10�6 4.59 � 10�6

22 3M 3.86 � 10�5 4.25 � 10�6 �2.41 � 10�5 5.12 � 10�6

23 Philip Morris 9.00 � 10�6 2.10 � 10�5 �1.08 � 10�5 9.62 � 10�6

24 Proctor & Gamble 4.22 � 10�5 4.10 � 10�6 1.84 � 10�5 4.12 � 10�6

25 Sears 1.42 � 10�5 5.49 � 10�6 1.38 � 10�5 4.47 � 10�6

26 Travelers 5.48 � 10�5 9.42 � 10�6 4.95 � 10�7 9.53 � 10�6

27 Union Carbide 1.46 � 10�5 4.84 � 10�6 1.24 � 10�5 7.56 � 10�6

28 United Technology 1.96 � 10�5 4.97 � 10�6 9.59 � 10�7 3.02 � 10�6

29 Wal-Mart 3.96 � 10�5 8.23 � 10�6 3.46 � 10�5 5.27 � 10�6

30 Disney 2.34 � 10�5 3.95 � 10�6 �3.61 � 10�6 5.21 � 10�6

To test for the presence of the autocorrelation characteristics in the5-min return series, the first-order autocorrelations are computed.Out of 30 securities, 26 securities have statistically significant atthe .01% level. The sample autocorrelations for lag up to 25 for rt, ,and are computed, and those for a subset of 30 stocks are reported inFigures 1 to 8. From these figures, it is apparent that all return seriesexhibit statistically significant serial correlations at the first lag, althoughautocorrelation decays more rapidly as the lag increases. The correspon-ding modified Box–Pierce statistics for the 30 stocks are presented inTable III. The p values for these Box–Pierce statistics are indistinguish-able from 0, indicating that these statistics are significant at the .01%level.

r˛

2t

0rt 0r̂1

(r̂1)


TABLE II

Sample Statistics for Intraday Returns (April 1, 1998 to June 30, 1998)

InterquartileExcess Range

I.D. No. N Skewness Kurtosis Maximum Minimum (IQR)

1 5093 �2.5366 164.25 5.54 � 10�2 �6.66 � 10�2 2.04 � 10�3

2 4938 .8318 32 3.88 � 10�2 �3.91 � 10�2 2.86 � 10�3

3 4976 3.688 72.4842 3.38 � 10�2 �2.27 � 10�2 1.70 � 10�3

4 4973 2.4355 42.4222 3.96 � 10�2 �1.90 � 10�2 1.29 � 10�3

5 5061 .3476 59.1833 3.99 � 10�2 �3.99 � 10�2 2.49 � 10�3

6 4975 2.3521 52.2514 4.89 � 10�2 �1.93 � 10�2 2.24 � 10�3

7 4968 .4645 21.018 2.15 � 10�2 �2.38 � 10�2 1.53 � 10�3

8 4924 2.8143 51.8403 5.13 � 10�2 �1.73 � 10�2 3.16 � 10�3

9 5024 .5018 18.4991 2.97 � 10�2 �2.32 � 10�2 1.71 � 10�3

10 5003 1.2956 24.2182 2.62 � 10�2 �1.81 � 10�2 1.77 � 10�3

11 5023 .4063 6.8106 1.7 � 10�2 �1.13 � 10�2 1.78 � 10�3

12 5115 .4206 36.6611 2.94 � 10�2 �3.17 � 10�2 1.49 � 10�3

13 5031 3.705 75.7613 4.54 � 10�2 �1.95 � 10�2 1.78 � 10�3

14 4969 �.3637 18.8361 1.37 � 10�2 �2.74 � 10�2 1.79 � 10�3

15 5062 .7705 40.0847 4.77 � 10�2 �3.58 � 10�2 2.05 � 10�3

16 5117 1.1779 28.7371 3.37 � 10�2 �2.05 � 10�2 1.20 � 10�3

17 4961 .8161 18.888 3.08 � 10�2 �2.63 � 10�2 2.47 � 10�3

18 4953 4.4414 110.7689 5.14 � 10�2 �1.99 � 10�2 1.78 � 10�3

19 5026 �.1624 18.34 2.05 � 10�2 �2.38 � 10�2 1.76 � 10�3

20 5035 .7487 55.4059 3.28 � 10�2 �3.17 � 10�2 1.93 � 10�3

21 5037 �.1048 75.2806 3.94 � 10�2 �3.89 � 10�2 1.93 � 10�3

22 4971 �5.5271 269.0492 4.27 � 10�2 �6.78 � 10�2 1.35 � 10�3

23 5156 .9676 55.99 5.11 � 10�2 �4.63 � 10�2 3.16 � 10�3

24 5011 �.2462 9.2984 1.29 � 10�2 �1.94 � 10�2 1.51 � 10�3

25 4989 .1144 11.1305 1.9 � 10�2 �2.64 � 10�2 2.10 � 10�3

26 5049 3.9582 417.1513 8.91 � 10�2 �9.1 � 10�2 2.02 � 10�3

27 4949 5.6157 181.9652 8.09 � 10�2 �4.29 � 10�2 2.45 � 10�3

28 4943 �.0551 8.868 1.4 � 10�2 �1.52 � 10�2 1.33 � 10�3

29 5028 .5303 17.7917 2.47 � 10�2 �2.19 � 10�2 2.3 � 10�3

30 5066 .5158 66.52 4.0 � 10�2 �3.66 � 10�2 1.17 � 10�3

642 Rahman

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FIGURE 1 Autocorrelation for Identification (I.D.) Number 5.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.41 3 5 7 9 11 13 15 17 19 21 23

lag

corr

elat

ion

R

|R|

R-square

FIGURE 2Autocorrelation for I.D. Number 11.

-0.28

-0.18

-0.08

0.02

0.12

0.22

0.32

0.42

1 3 5 7 9 11 13 15 17 19 21 23

lag

corr

elat

ion

Lag

R

|R|

R-square

These results are evidence that the 5-min returns tend not to beindependent but instead exhibit volatility clustering, where periods oflarge absolute changes tend to cluster together followed by periods ofrelatively small absolute changes. This implies that large returns tend tobe followed by large returns (of either sign), whereas small returns tendto be followed by small returns. This suggests that the usual measures

644 Rahman


-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1 3 5 7 9 11 13 15 17 19 21 23

lag

corr

elat

ion

R

|R|

R-square


-0.2

-0.1

0

0.1

0.2

0.3

0.4

1 3 5 7 9 11 13 15 17 19 21 23

lag

corr

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ion

Lag

R

|R|

R-square

of return volatility are temporally dependent (heteroskedastic). In sum-mary, the data display all the characteristics of the unconditional distri-bution of returns that are used to justify fitting the GARCH model to thereturn series. Moreover, because the autocorrelation for each of theseries cuts off after one lag, the GARCH (1,1) appears to be an appropri-ate model.



-0.18

-0.08

0.02

0.12

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0.32

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1 3 5 7 9 11 13 15 17 19 21 23

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corr

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R

|R|

R-square


-0.38

-0.28

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0.12

0.22

0.32

0.42

1 3 5 7 9 11 13 15 17 19 21 23

lag

corr

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ion

Lag

R

|R|

R-square

Table IV presents the results of fitting the GARCH (1,1) process tothe 5-min return series of each of the 30 DJIA stocks for both the prefu-tures and postfutures period. Most of the parameter estimates of theGARCH (1,1) model in the table are statistically significant at the .01%level. The estimates of ao are all positive and considerably smaller thanthe sample variances shown in Table I. This is due to changing

646 Rahman

FIGURE 7 Autocorrelation for I.D. Number 26.

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1 3 5 7 9 11 13 15 17 19 21 23

lag

corr

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R

|R|

R-square


-0.3

-0.2

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conditional variances over time and their eventual contribution tounconditional variances. The persistence in volatility, as measured by thesum of a1 and a2 in GARCH (1,1), is closer to unity for several of thesecurities. The fact that the sums of a1 and a2 are fairly close to 1 indi-cates the persistence of past volatility in explaining current volatility (seeEngle & Bollerslev, 1986).


TABLE IV

GARCH Model Estimates of Equation 1

1997 1998

Security a1 a2 a1 a2

1 �.37574 � 10�3 0.000 .42116* 0.00(�.4734) (0.000) (11.39) (0.00)

2 .94623 � 10�1* .73222* .16976* 0.00(7.614) (22.72) (7.738) (0.00)

3 .72152 � 10�1 �.27785 � 10�2 .18215* 0.00(1.173) (�1.162) (7.760) (0.00)

4 .13806* .81371* .16179* .80951*(13.27) (75.73) (13.52) (79.75)

5 .17240 � 10�3 .982 � 10�2 .52302 �.23662 � 10�3

(3.33) (.5779 � 10�2) (1.84) (�.6322)6 .11084* .66648* .18386* .72961*

(9.435) (34.07) (12.06) (41.00)7 .14706* .53187 � 10�5 .15544* 0.00

(38.27) (3.429) (7.748) (0.00)8 �.17242 � 10�3 .99608* .9562 � 10�1* .37747*

(.2451 � 10�1) (2407) (5.658) (4.848)9 .047072* .78194 � 10�1* .29986 � 10�1 0.00

(39.15) (17.63) (2.409) (0.00)10 .10694* .67562* .27231* 0.00

(7.622) (20.68) (10.29) (0.00)11 �.21094 � 10�3 .1013 � 10�1 .10856* .74386*

(.4689) (.7197 � 10�2) (8.571) (26.84)12 .061375* .11995* .28299* .12236

(40.34) (17.33) (10.57) (3.419)13 .77921 � 10�1* .53222* .11207* .70979*

(5.353) (8.307) (6.11) (24.92)14 .57935* .50306 � 10�3 .21237* .71976*

(45.05) (1.339) (12.22) (44.02)15 .13838* 0.00 1.2379* .28757*

(5.237) (0.00) (18.71) (14.62)16 .029512* .45815* .18268 �.57918 � 10�3

(41.23) (5.245) (1.034) (�.6447)17 .14103* .65857* .10689* .75881*

(8.807) (19.47) (8.709) (32.23)18 .57074* .35283 � 10�3 .29208* �.21323 � 10�2

(46.84) (1.321) (10.13) (�.7555)19 .63731 � 10�1* 0.00 .13343* .69618*

(4.391) (0.00) (9.298) (27.53)20 .49979 0.000 .27239* 0.00

(1.408) (0.000) (10.42) (0.00)21 .49979 0.000 �.38246 � 10�3* 0.00

(2.336) (0.000) (�21.22) (0.00)22 .18301* .69598* .51959* .94248 � 10�2

(11.42) (33.07) (12.24) (1.057)23 �.14238 � 10�3 0.000 .16542 �.11839 � 10�2

(�1.583) (0.000) (1.109) (�1.106)24 .16666* 0.00 1.0201* .4407 � 10�3*

(8.307) (0.00) (49.80) (3.995)

(Continued)

648 Rahman

TABLE IV

(Continued)

1997 1998

Security a1 a2 a1 a2

25 �.17402 �.19402 .93364 � 10�1* 0.00(�.7015 � 10�8) (0.000) (5.732) (0.00)

26 1.6337* .59129 � 10�4 2.7806* .61095 � 10�1*(21.07) (.1475) (24.36) (6.822)

27 .12252* 0.00 .7589 � 10�1* �.18538 � 10�2

(6.77) (0.00) (4.448) (�.1113)28 .90074 � 10�1* .47852* .86425 � 10�1* .81164*

(6.644) (18.13) (9.135) (42.00)29 .18422* .43311* .11717* 0.00

(10.46) (8.511) (6.584) (0.00)30 .77921 � 10�1* .53222* .28020* 0.00

(5.353) (8.307) (9.245) (0.00)

*Significant at the .01% level.

The contention that the introduction of futures and futures optionson the DJIA could increase volatility in the 30 stocks comprising theDJIA is essentially a hypothesis that derivatives trading alters the param-eters of conditional volatility of intraday returns. In Table IV, a casualcomparison of the distribution of estimated parameters of conditionalvolatility for the prefutures and postfutures periods suggests that theseparameters did not change significantly in aggregate subsequent to theintroduction of derivatives. To determine this more precisely, a pairedcomparison test for the significance of the differences in the estimatedparameters for the two periods is employed. The test is conducted for all30 stocks together with the following test statistic described in Harnettand Soni (1991):

(2)

where and are the sample means of a given parameter (e.g.,either a1 or a2) for all 30 stocks for the prefutures and postfutures peri-od, respectively; and are the respective sample variances; mpre andmpost are the respective population means; and npre and npost are thesample sizes for prefutures and postfutures periods. In particular,the purpose of this test is to draw a conclusion about the average

s2posts2

pre

xpostxpre

tc �(xpre � xpost) � (mpre � mpost)

Ba(npre � 1)s2

pre

npre � npost � 2�

(npost � 1)s2post

npre � npost � 2b a 1

npre�

1npostb

behavior of volatility of the group of 30 stocks before and after theintroduction of derivatives. The test statistic is distributed as a t distribu-tion with (npre � npost � 2) degrees of freedom.

The test statistics for a1, a2, and a1 � a2 are computed for all30 stocks together by the consideration of estimated parameters for bothperiods. The term a1 � a2 measures persistence in volatility. The calcu-lated test statistics for a1, a2, and a1 � a2 are �1.80, 0.33, and �1.28,respectively. These values are not large enough to reject the null hypoth-esis of no shift in the estimated parameters from prefutures to postfu-tures periods at the .01% significance level. These results suggest thatthe introduction of index futures and futures options on the DJIA hasproduced no structural changes on the conditional volatility in the spotmarket. This implies that the data examined here do not validate thecontention that the introduction of derivatives trading has increasedvolatility in the spot market.

It is interesting to note that two other financial-derivative productsbased on the DJIA were introduced in the market about the same timethe CBOT started trading the DJIA index futures and futures options.The Chicago Board Option Exchange introduced an index option on theDJIA on October 6, 1997. On January 20, 1998, the American StockExchange introduced the DIAMONDS, securities that allow investors totrade shares in an entire portfolio of the DJIA as easily as they do sharesof a single stock. These products may affect trading activities (and there-by volatility) in the DJIA stocks. Nonoverlapping prefutures and postfu-tures samples in this study coincide with the periods before and after theintroduction of these two products. The results of this study do not indi-cate any change in spot market volatility between these sample periods.This suggests that the DJIA index futures and futures options along withthe DJIA index options and the DIAMONDS do not cause increasedspot market volatility.

CONCLUSION

This article examines the impact of trading in the DJIA index futures onthe volatility of the underlying spot market of component stocks. Itinvestigates the contention that the introduction of futures and futuresoptions on the DJIA increases volatility in the 30 stocks comprising theDJIA. Intraday return data on these stocks for April through June 1997(prefutures period) and April through June 1998 (postfutures period) areused. The distributional properties of the intraday return series are firstexamined to determine whether the GARCH model can characterize the


return series. The GARCH (1,1) model appears to be an appropriatemodel for intraday return series. The GARCH (1,1) model is employedto estimate the conditional volatility of intraday returns. Parameters ofconditional volatility of prefutures and postfutures periods are estimatedwith the GARCH (1,1) model and compared to determine if the estimat-ed parameters have, in aggregate, changed significantly after the intro-duction of derivatives. On the basis of empirical results, the null hypoth-esis of no change in conditional volatility from prefutures to postfuturesperiods cannot be rejected.

These findings are important because supporters of restrictions onindex futures trading maintain that these derivatives increase volatility,thereby increasing the cost of capital. The empirical evidence that theconditional volatility of component stocks has not changed with theintroduction of derivatives suggests that these arguments lack merit.Thus, the argument that the introduction of derivatives destabilizes thespot market appears to be unfounded. Consequently, calls for closer reg-ulation of index futures on the basis that they increase spot marketvolatility are unjustified. These regulations are not likely to contribute toa more stable environment in the spot market. On the contrary, theseregulations may be counterproductive because they may divert attentionaway from more relevant and urgently needed policy options, researchefforts, or both.

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